Not entirely what you want but you can use the same installation by setting up sub-forums. Each sub forum can have it's own style to distinguish it from the others which would make it appear to be separate. If you need to restrict access you can set up usergroups for each sub forum. Instead of having to register for separate forums they could instead register once and request permission to join the usergroup.
“Results! Why, man, I have gotten a lot of results! I have found several thousand things that won’t work.”
Attributed - Thomas Edison